THE MEASURE OF DISPERSION

The Measure of Dispersion

The measure of dispersion refers to the spread of data in a
given distribution. The measures of dispersion are range, mean
deviation, variance and standard deviation.

The Range

This is the difference between the highest value and lowest value in a
given distribution.

Range : Hi – Li e.g 12,15, 10,16, 20 Hi = 20 Li = 10 Range : 20 –
10 = 10, e.g , 10 – 20, ……..60- 70 , 80 – 90 . range = Hi – Li , Li = 10 Hi=
90 . 90 – 10 = 80

Advantages/Merits of the Range

i. It is easy to understand
ii. It is easy to calculate or compute
iii. It is useful for further statistical calculation

Disadvantages / Demerits of the Range

i. It does not consider all values in the distribution , only the
extremes values are used
ii. It is not a reliable measure of veriability

, Mean deviation :Mean deviation may be defined as the
arithmetic mean of all absolute deviations from the mean .
⎺ /¿
Formula of mean deviation ( simple data ) ---- £¿ x−x n
¿

⎺/¿
Formula of mean deviation (grouped data )------ £ f / x−x
£f
¿




Variance and Standard deviation

VARIANCE: This can be described as the average of square of
the deviation .

Variance formula simple data S2=
£ ( x−x ⎺)2 ( x−x ⎺)2
. formula ( Grouped data ) S 2=∑ ❑ F
n £f

THE STANDARD DEVIATION
£ F ( x−x ⎺) 2
FORMULA of grouped data S= £f



The standard deviation may be defined as the square root of the
variance or mean of the square deviation from the arithmetic mean of
the distribution .
( x−x ⎺ )2
Formula: √❑ ∑ n
------- simple data

Formula : ∑ f
√ ( x−x ⎺ ) 2
£f
--------- Grouped data